Theorem eqrelriiv

Description: Inference from extensionality principle for relations. (Contributed by NM, 17-Mar-1995)

	Ref	Expression
Hypotheses	eqreliiv.1	|- Rel A
	eqreliiv.2	|- Rel B
	eqreliiv.3	|- ( <. x , y >. e. A <-> <. x , y >. e. B )
Assertion	eqrelriiv	|- A = B

Proof

Step	Hyp	Ref	Expression
1		eqreliiv.1	|- Rel A
2		eqreliiv.2	|- Rel B
3		eqreliiv.3	|- ( <. x , y >. e. A <-> <. x , y >. e. B )
4	3	eqrelriv	|- ( ( Rel A /\ Rel B ) -> A = B )
5	1 2 4	mp2an	|- A = B